Many daily tasks require a little bit of organization. For example, you would not want your coffee poured before you got your cup. Some tasks simply need to take precedence before other tasks, otherwise you might get into a mess. This becomes particularly apparent if you try to teach a robot how to help with such tasks. In this chapter, we investigate partial orders and lattices, which allow one to abstract the precedence relation of tasks. Partial orders are absolutely fundamental in mathematical arguments, and they have many applications in computer science.